The 'Potters' took a point away from the King Power Stadium on Saturday after a Jack Butland howler cancelled out Xherdan Shaqiri's first-half strike.
However, Stoke remain in the relegation zone and are one point from safety but with things so close between the bottom-half teams, Lambert believes his side are playing well enough to stay up.
Speaking after the game, the boss said: "It's frustrating not to get three points but I could say the same [about the matches] against Brighton and Bournemouth."
"Since we came in we've only won one game but we've always been in games, which is important for us, to compete. We need a bit of a break, like every other team, but if we keep playing the way we are then we'll certainly climb the table".
He continued: "The good thing for me is we are playing ever so well. We've only been beaten once since I came in and we've had some really hard games. Performance-wise we can match anyone in the division and with a little bit of a break we will certainly win games. Anybody coming to our games in the last few weeks would see Stoke City as a good side."
Their next league fixture is against Southampton, who also secured a point on Saturday against middle-of-the-table Burnley.